Bootstraps for Time Series

Peter Bühlmann

July 1999

Abstract

We compare and review block, sieve and local bootstraps for time series and thereby illuminate theoretical facts as well as performance on finite-sample data. Our (re-) view is {\em selective} with the intention to get a new and fair picture about some particular aspects of bootstrapping time series. The generality of the block bootstrap is contrasted by sieve bootstraps. We discuss implementational dis-/advantages and argue that two types of sieves outperform the block method, each of them in its own important niche, namely linear and categorical processes, respectively. Local bootstraps, designed for nonparametric smoothing problems, are easy to use and implement but exhibit in some cases low performance.

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